I would recommend using a filter to do the job as described in the filtering and paging data documentation. You can create a custom filter which will be basically just the drop down list. You can take inspiration in the existing "Page name filter" web part.
Or, another option would be adding some query string parameter to the URL - e.g. the drop down change event will add the parameter to the URL and in the repeater's WHERE condition you will use query string macro to read the value. Do not forget to supply default value in case parameter is missing, do not forget to sanitize the input to avoid SQLi.